{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 解方程\n",
    "\n",
    "## 简单的一元一次方程\n",
    "\n",
    "\n",
    "\\begin{equation}x + 16 = -25\\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}x + 16 - 16 = -25 - 16\\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}x = -25 - 16\\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}x = -41\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = -41                # 验证方程的解\n",
    "x + 16 == -25"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 带系数的方程\n",
    "\n",
    "\\begin{equation}3x - 2 = 10 \\end{equation}\n",
    "\n",
    "\\begin{equation}3x - 2 + 2 = 10 + 2 \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}3x = 12 \\end{equation}\n",
    "\n",
    "\\begin{equation}x = 4\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 4                  # 代入 x = 4\n",
    "3 * x - 2 == 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 系数是分数的方程\n",
    "\n",
    "\\begin{equation}\\frac{x}{3} + 1 = 16 \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}\\frac{x}{3} = 15 \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}\\frac{3}{1} \\cdot \\frac{x}{3} = 15 \\cdot 3 \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}x = 45 \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 45\n",
    "x/3 + 1 == 16"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 需要合并同类项的例子\n",
    "\n",
    "\\begin{equation}3x + 2 = 5x - 1 \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}3x + 3 = 5x \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}3 = 2x \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}\\frac{3}{2} = x \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}x = \\frac{3}{2} \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}x = 1\\frac{1}{2} \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 1.5\n",
    "3*x + 2 == 5*x -1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 一元方程练习\n",
    "\n",
    "\\begin{equation}\\textbf{4(x + 2)} + \\textbf{3(x - 2)} = 16 \\end{equation}\n",
    "\n",
    "\\begin{equation}4x + 8 + 3x - 6 = 16 \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}7x + 2 = 16 \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}7x = 14 \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}\\frac{7x}{7} = \\frac{14}{7} \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}x = 2 \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 2\n",
    "4 * (x + 2) + 3 * (x - 2) == 16"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 线性方程\n",
    "\n",
    "\n",
    "## 例子\n",
    "\n",
    "\n",
    "\\begin{equation}2y + 3 = 3x - 1 \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}2y + 4 = 3x \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}2y = 3x - 4 \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}y = \\frac{3x - 4}{2} \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  x      y\n",
      "---  -----\n",
      "-10  -17\n",
      " -9  -15.5\n",
      " -8  -14\n",
      " -7  -12.5\n",
      " -6  -11\n",
      " -5   -9.5\n",
      " -4   -8\n",
      " -3   -6.5\n",
      " -2   -5\n",
      " -1   -3.5\n",
      "  0   -2\n",
      "  1   -0.5\n",
      "  2    1\n",
      "  3    2.5\n",
      "  4    4\n",
      "  5    5.5\n",
      "  6    7\n",
      "  7    8.5\n",
      "  8   10\n",
      "  9   11.5\n",
      " 10   13\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from tabulate import tabulate\n",
    "\n",
    "x = np.array(range(-10, 11))  # 从 -10 到 10 的21个数据点\n",
    "y = (3 * x - 4) / 2           # 对应的函数值\n",
    "\n",
    "print(tabulate(np.column_stack((x,y)), headers=['x', 'y']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = \"last_expr\"\n",
    "# %matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "plt.plot(x, y, color=\"grey\", marker = \"o\")\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 截距"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, color=\"grey\")\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid()\n",
    "plt.axhline()                # 画出坐标轴\n",
    "plt.axvline()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- x轴上的截距\n",
    "\n",
    "\\begin{equation}0 = \\frac{3x - 4}{2} \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}\\frac{3x - 4}{2} = 0 \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}3x - 4 = 0 \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}3x = 4 \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}x = \\frac{4}{3} \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}x = 1\\frac{1}{3} \\end{equation}\n",
    "\n",
    "- y轴上的截距\n",
    "\n",
    "\\begin{equation}y = \\frac{3\\cdot0 - 4}{2} \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}y = \\frac{-4}{2} \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}y = -2 \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, color=\"grey\")\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid()\n",
    "plt.axhline()\n",
    "plt.axvline()\n",
    "plt.annotate('x',(1.333, 0)) # 标出截距点\n",
    "plt.annotate('y',(0,-2))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "> 截距的作用是明显的：两点成一线。连接截距就可以画出函数曲线。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 斜率\n",
    "\n",
    "\\begin{equation}slope = \\frac{\\Delta{y}}{\\Delta{x}} \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}m = \\frac{y_{2} - y_{1}}{x_{2} - x_{1}} \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}m = \\frac{7 - -2}{6 - 0} \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}m = \\frac{7 + 2}{6 - 0} \\end{equation}\n",
    "\n",
    "\\begin{equation}m = 1.5 \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, color=\"grey\")\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid()\n",
    "plt.axhline()\n",
    "plt.axvline()\n",
    "m = 1.5\n",
    "xInt = 4 / 3\n",
    "yInt = -2\n",
    "mx = [0, xInt]\n",
    "my = [yInt, yInt + m * xInt]\n",
    "plt.plot(mx, my, color='red', lw=5)  # 用红色标出\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.grid()                             # 放大图\n",
    "plt.axhline()\n",
    "plt.axvline()\n",
    "m = 1.5\n",
    "xInt = 4 / 3\n",
    "yInt = -2\n",
    "mx = [0, xInt]\n",
    "my = [yInt, yInt + m * xInt]\n",
    "plt.plot(mx, my, color='red', lw=5) \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 直线的斜率、截距形式\n",
    "\n",
    "\\begin{equation}y = mx + b \\end{equation}\n",
    "\n",
    "\\begin{equation}y = \\frac{3x - 4}{2} \\end{equation}\n",
    "\n",
    "\\begin{equation}y = 1\\frac{1}{2}x + -2 \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = 1.5\n",
    "yInt = -2\n",
    "\n",
    "x = np.array(range(-10, 11))\n",
    "y2 = m * x + yInt                       # 斜率截距形式\n",
    "\n",
    "plt.plot(x, y2, color=\"grey\")\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid()\n",
    "plt.axhline()\n",
    "plt.axvline()\n",
    "\n",
    "plt.annotate('y', (0, yInt))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 线形方程组\n",
    "> 解的含义：直线的交点\n",
    "\n",
    "\\begin{equation}x + y = 16 \\end{equation}\n",
    "\\begin{equation}10x + 25y = 250 \\end{equation}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "l1p1 = [16, 0]  # 线1点1\n",
    "l1p2 = [0, 16]  # 线1点2\n",
    "\n",
    "\n",
    "l2p1 = [25,0]   # 线2点1\n",
    "l2p2 = [0,10]   # 线2点2\n",
    "\n",
    "\n",
    "plt.plot(l1p1,l1p2, color='blue')\n",
    "plt.plot(l2p1, l2p2, color=\"orange\")\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 解线形方程组 （消去法）\n",
    "\\begin{equation}x + y = 16 \\end{equation}\n",
    "\\begin{equation}10x + 25y = 250 \\end{equation}\n",
    "\n",
    "\\begin{equation}-10(x + y) = -10(16) \\end{equation}\n",
    "\\begin{equation}10x + 25y = 250 \\end{equation}\n",
    "\n",
    "\\begin{equation}-10x + -10y = -160 \\end{equation}\n",
    "\\begin{equation}10x + 25y = 250 \\end{equation}\n",
    "\n",
    "\\begin{equation}15y = 90 \\end{equation}\n",
    "\\begin{equation}y = \\frac{90}{15} \\end{equation}\n",
    "\\begin{equation}y = 6 \\end{equation}\n",
    "\n",
    "\\begin{equation}x + 6 = 16 \\end{equation}\n",
    "\\begin{equation}x = 10 \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "x = 10\n",
    "y = 6\n",
    "print ((x + y == 16) & ((10 * x) + (25 * y) == 250))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 指数、根和对数\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "\n",
    "## 指数\n",
    "\\begin{equation}2^{2} = 2 \\cdot 2 = 4\\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}2^{3} = 2 \\cdot 2 \\cdot 2 = 8\\end{equation}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "125\n"
     ]
    }
   ],
   "source": [
    "x = 5**3\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 根\n",
    "\n",
    "\\begin{equation}?^{2} = 9 \\end{equation}\n",
    "\n",
    "\\begin{equation}\\sqrt{9} = 3 \\end{equation}\n",
    "\n",
    "\\begin{equation}\\sqrt[3]{64} = 4 \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.0\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "x = math.sqrt(9)            # 平方根\n",
    "print (x)\n",
    "\n",
    "cr = round(64 ** (1. / 3))   # 立方根\n",
    "print(cr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 根是分数形式的指数\n",
    "\n",
    "\\begin{equation} 8^{\\frac{1}{3}} = \\sqrt[3]{8} = 2 \\end{equation}\n",
    "\n",
    "\\begin{equation} 9^{\\frac{1}{2}} = \\sqrt{9} = 3 \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.0\n",
      "3.0\n"
     ]
    }
   ],
   "source": [
    "print (9**0.5)\n",
    "print (math.sqrt(9))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 对数\n",
    "> 对数是指数的逆运算\n",
    "\n",
    "\\begin{equation}4^{?} = 16 \\end{equation}\n",
    "\n",
    "\\begin{equation}log_{4}(16) = 2 \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.0\n"
     ]
    }
   ],
   "source": [
    "x = math.log(16, 4)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 以10为底的对数\n",
    "\n",
    "\\begin{equation}log(64) = 1.8061 \\end{equation}\n",
    "\n",
    "### 自然对数\n",
    "\\begin{equation}log_{e}(64) = ln(64) = 4.1589 \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.806179973983887\n",
      "4.1588830833596715\n"
     ]
    }
   ],
   "source": [
    "print(math.log10(64))\n",
    "\n",
    "print (math.log(64))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 幂运算 （合并同类项）\n",
    "\n",
    "\\begin{equation}2y = 2x^{4} ( \\frac{x^{2} + 2x^{2}}{x^{3}} ) \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}2y = 2x^{4} ( \\frac{3x^{2}}{x^{3}} ) \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}2y = 2x^{4} ( 3x^{-1} ) \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}2y = 6x^{3} \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}y = 3x^{3} \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  x      y\n",
      "---  -----\n",
      "-10  -3000\n",
      " -9  -2187\n",
      " -8  -1536\n",
      " -7  -1029\n",
      " -6   -648\n",
      " -5   -375\n",
      " -4   -192\n",
      " -3    -81\n",
      " -2    -24\n",
      " -1     -3\n",
      "  0      0\n",
      "  1      3\n",
      "  2     24\n",
      "  3     81\n",
      "  4    192\n",
      "  5    375\n",
      "  6    648\n",
      "  7   1029\n",
      "  8   1536\n",
      "  9   2187\n",
      " 10   3000\n"
     ]
    }
   ],
   "source": [
    "x = np.array(range(-10, 11))\n",
    "y3 = 3 * x ** 3\n",
    "\n",
    "print(tabulate(np.column_stack((x, y3)), headers=['x', 'y']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y3, color=\"magenta\")  # y3是曲线\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid()\n",
    "plt.axhline()\n",
    "plt.axvline()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 看一个成指数增长的例子\n",
    "\n",
    "\\begin{equation}y = 2^{x} \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y4 = 2.0**x\n",
    "plt.plot(x, y4, color=\"magenta\")\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid()\n",
    "plt.axhline()\n",
    "plt.axvline()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 复利计算\n",
    "\n",
    "> 存款100，年利5%，20年后余额是多少（记复利）\n",
    "\n",
    "\\begin{equation}y1 = 100 + (100 \\cdot 0.05) \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}y1 = 100 \\cdot 1.05 \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}y2 = 100 \\cdot 1.05 \\cdot 1.05 \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}y2 = 100 \\cdot 1.05^{2} \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}y20 = 100 \\cdot 1.05^{20} \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "year = np.array(range(1, 21))                      # 年份\n",
    "balance = 100 * (1.05 ** year)                     # 余额\n",
    "plt.plot(year, balance, color=\"green\")\n",
    "plt.xlabel('Year')\n",
    "plt.ylabel('Balance')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 多项式\n",
    "\n",
    "\\begin{equation}12x^{3} + 2x - 16 \\end{equation}\n",
    "\n",
    "三项：\n",
    "- 12x<sup>3</sup>\n",
    "- 2x\n",
    "- -16\n",
    "\n",
    "\n",
    "- 两个系数(12 和 2) 和一个常量-16\n",
    "- 变量 x\n",
    "- 指数 <sup>3</sup>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 标准形式\n",
    "随着x的指数增长排列（升幂）\n",
    "\\begin{equation}3x + 4xy^{2} - 3 + x^{3} \\end{equation}\n",
    "\n",
    "指数最高项在前（降幂）\n",
    "\\begin{equation}x^{3} + 4xy^{2} + 3x - 3 \\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "\n",
    "## 多项式化简\n",
    "\n",
    "\n",
    "\\begin{equation}x^{3} + 2x^{3} - 3x - x + 8 - 3 \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}3x^{3} - 4x + 5 \\end{equation}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from random import randint\n",
    "x = randint(1,100)                  # 取任意值验证多项式化简\n",
    "\n",
    "(x**3 + 2*x**3 - 3*x - x + 8 - 3) == (3*x**3 - 4*x + 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 多项式相加\n",
    "\n",
    "\\begin{equation}(3x^{3} - 4x + 5)   +   (2x^{3} + 3x^{2} - 2x + 2) \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}3x^{3} + 2x^{3} + 3x^{2} - 4x -2x + 5 + 2 \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}5x^{3} + 3x^{2} - 6x + 7 \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = randint(1,100)\n",
    "\n",
    "\n",
    "(3*x**3 - 4*x + 5) + (2*x**3 + 3*x**2 - 2*x + 2) == 5*x**3 + 3*x**2 - 6*x + 7"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 多项式相减\n",
    "\n",
    "\\begin{equation}(2x^{2} - 4x + 5)   -   (x^{2} - 2x + 2) \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}(2x^{2} - 4x + 5)   +   (-x^{2} + 2x - 2) \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}2x^{2} + -x^{2} + -4x + 2x + 5 + -2 \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}x^{2} - 2x + 3 \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from random import randint\n",
    "x = randint(1,100)\n",
    "\n",
    "(2*x**2 - 4*x + 5) - (x**2 - 2*x + 2) == x**2 - 2*x + 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 多项式相乘\n",
    "\n",
    "1. 用第一个多项式的每一项乘以第二个多项式\n",
    "2. 把相乘的结果合并同类项\n",
    "\n",
    "\n",
    "\\begin{equation}(x^{4} + 2)(2x^{2} + 3x - 3) \\end{equation}\n",
    "\n",
    "\\begin{equation}2x^{6} + 3x^{5} - 3x^{4} + 4x^{2} + 6x - 6 \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = randint(1,100)\n",
    "\n",
    "(x**4 + 2)*(2*x**2 + 3*x - 3) == 2*x**6 + 3*x**5 - 3*x**4 + 4*x**2 + 6*x - 6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 多项式相除\n",
    "\n",
    "### 简单例子\n",
    "\n",
    "\\begin{equation}(4x + 6x^{2}) \\div 2x \\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}\\frac{4x + 6x^{2}}{2x} \\end{equation}\n",
    "\n",
    "\\begin{equation}\\frac{4x}{2x} + \\frac{6x^{2}}{2x}\\end{equation}\n",
    "\n",
    "\\begin{equation}2 + 3x\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = randint(1,100)\n",
    "\n",
    "(4*x + 6*x**2) / (2*x) == 2 + 3*x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 长除法\n",
    "\n",
    "\\begin{equation}(x^{2} + 2x - 3) \\div (x - 2) \\end{equation}\n",
    "\n",
    "\\begin{equation} x - 2 |\\overline{x^{2} + 2x - 3} \\end{equation}\n",
    "\n",
    "\\begin{equation} \\;\\;\\;\\;x \\end{equation}\n",
    "\\begin{equation}x - 2 |\\overline{x^{2} + 2x - 3} \\end{equation}\n",
    "\\begin{equation} \\;x^{2} -2x \\end{equation}\n",
    "\n",
    "\\begin{equation} \\;\\;\\;\\;x \\end{equation}\n",
    "\\begin{equation}x - 2 |\\overline{x^{2} + 2x - 3} \\end{equation}\n",
    "\\begin{equation}- (x^{2} -2x) \\end{equation}\n",
    "\\begin{equation}\\;\\;\\;\\;\\;\\overline{\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;4x -3} \\end{equation}\n",
    "\n",
    "\\begin{equation} \\;\\;\\;\\;\\;\\;\\;\\;x + 4 \\end{equation}\n",
    "\\begin{equation}x - 2 |\\overline{x^{2} + 2x - 3} \\end{equation}\n",
    "\\begin{equation}- (x^{2} -2x) \\end{equation}\n",
    "\\begin{equation}\\;\\;\\;\\;\\;\\overline{\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;4x -3} \\end{equation}\n",
    "\\begin{equation}- (\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;4x -8) \\end{equation}\n",
    "\\begin{equation}\\;\\;\\;\\;\\;\\overline{\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;5} \\end{equation}\n",
    "\n",
    "\\begin{equation}x + 4 + \\frac{5}{x-2} \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = randint(3,100)\n",
    "\n",
    "(x**2 + 2*x -3)/(x-2) == x + 4 + (5/(x-2))\n",
    "                                "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# 因式\n",
    "\n",
    "\n",
    "16可以如下表示\n",
    "- 1 x 16\n",
    "- 2 x 8\n",
    "- 4 x 4\n",
    "\n",
    "或者 1, 2, 4, 8 是 16 的因子\n",
    "\n",
    "## 用多项式乘来表示多项式\n",
    "\n",
    "\\begin{equation}-6x^{2}y^{3} \\end{equation}\n",
    "\n",
    "\\begin{equation}(2xy^{2})(-3xy) \\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "又如\n",
    "\n",
    "\\begin{equation}(x + 2)(2x^{2} - 3y + 2) = 2x^{3} + 4x^{2} - 3xy + 2x - 6y + 4 \\end{equation}\n",
    "\n",
    "那么**x+2** 和 **2x<sup>2</sup> - 3y + 2** 都是 **2x<sup>3</sup> + 4x<sup>2</sup> - 3xy + 2x - 6y + 4**的因子"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 最大公共因子\n",
    "\n",
    "|   16   |   24   |\n",
    "|--------|--------|\n",
    "| 1 x 16 | 1 x 24 |\n",
    "| 2 x 8 | 2 x 12 |\n",
    "| 2 x **8**  | 3 x **8**  |\n",
    "| 4 x 4  | 4 x 6  |\n",
    "\n",
    "8是16和24的最大公约数\n",
    "\n",
    "\n",
    "\\begin{equation}15x^{2}y\\;\\;\\;\\;\\;\\;\\;\\;9xy^{3}\\end{equation}\n",
    "\n",
    "这两个多项式的最大公共因子是?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 最大公共因子\n",
    "\n",
    "先看系数，他们都包含**3** \n",
    "- 3 x 5 = 15  \n",
    "- 3 x 3 = 9\n",
    "\n",
    "\n",
    "再看***x***项， x<sup>2</sup> 和 x。\n",
    "\n",
    "最后看***y***项, y 和 y<sup>3</sup>。\n",
    "\n",
    "\n",
    "最大公共因子是\n",
    "\\begin{equation}3xy\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 最大公共因子\n",
    "\n",
    "可见最大公共因子总包括\n",
    "\n",
    "- 系数的最大公约数\n",
    "- 变量指数的最小值\n",
    "\n",
    "用多项式除来验证：\n",
    "\n",
    "\\begin{equation}\\frac{15x^{2}y}{3xy}\\;\\;\\;\\;\\;\\;\\;\\;\\frac{9xy^{3}}{3xy}\\end{equation}\n",
    "\n",
    "\\begin{equation}3xy(5x) = 15x^{2}y\\end{equation}\n",
    "\\begin{equation}3xy(3y^{2}) = 9xy^{3}\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "x = randint(1,100)\n",
    "y = randint(1,100)\n",
    "\n",
    "print((3*x*y)*(5*x) == 15*x**2*y)\n",
    "print((3*x*y)*(3*y**2) == 9*x*y**3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 用系数最大公约数作因式分解\n",
    "\n",
    "\\begin{equation}6x + 15y \\end{equation}\n",
    "\n",
    "\\begin{equation}6x + 15y = 3(2x) + 3(5y) \\end{equation}\n",
    "\n",
    "\\begin{equation}6x + 15y = 3(2x) + 3(5y) = \\mathbf{3(2x + 5y)} \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = randint(1,100)\n",
    "y = randint(1,100)\n",
    "\n",
    "(6*x + 15*y) == (3*(2*x) + 3*(5*y)) == (3*(2*x + 5*y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 用最大公共因子作因式分解\n",
    "\\begin{equation}15x^{2}y + 9xy^{3}\\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}3xy(5x) = 15x^{2}y\\end{equation}\n",
    "\\begin{equation}3xy(3y^{2}) = 9xy^{3}\\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}15x^{2}y + 9xy^{3} = \\mathbf{3xy(5x + 3y^{2})}\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = randint(1,100)\n",
    "y = randint(1,100)\n",
    "\n",
    "(15*x**2*y + 9*x*y**3) == (3*x*y*(5*x + 3*y**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 用平方差公式作因式分解\n",
    "\n",
    "\\begin{equation}x^{2} - 9\\end{equation}\n",
    "\n",
    "\\begin{equation}x^{2} - 3^{2}\\end{equation}\n",
    "\n",
    "\\begin{equation}(x - 3)(x + 3)\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = randint(1,100)\n",
    "\n",
    "(x**2 - 9) == (x - 3)*(x + 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 用平方作因式分解\n",
    "\\begin{equation}x^{2} + 10x + 25\\end{equation}\n",
    "\n",
    "\\begin{equation}(x + 5)(x + 5)\\end{equation}\n",
    "\n",
    "\\begin{equation}(x + 5)^{2}\\end{equation}\n",
    "\n",
    "一般的\n",
    "\\begin{equation}(a + b)^{2} = a^{2} + b^{2}+ 2ab \\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = randint(1,100)\n",
    "b = randint(1,100)\n",
    "\n",
    "a**2 + b**2 + (2*a*b) == (a + b)**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# 二次方程\n",
    "\n",
    "\\begin{equation}y = 2(x - 1)(x + 2)\\end{equation}\n",
    "\n",
    "\\begin{equation}y = 2x^{2} + 2x - 4\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.array(range(-9, 9))\n",
    "y = 2 * x **2 + 2 * x - 4\n",
    "plt.plot(x, y, color=\"grey\")  # 画二次曲线 （抛物线）\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid()\n",
    "plt.axhline()\n",
    "plt.axvline()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    ">会是什么形状？\n",
    "\n",
    "\\begin{equation}y = -2x^{2} + 6x + 7\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.array(range(-8, 12))\n",
    "y = -2 * x ** 2 + 6 * x + 7\n",
    "plt.plot(x, y, color=\"grey\")\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid()\n",
    "plt.axhline()\n",
    "plt.axvline()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 抛物线的顶点\n",
    "\\begin{equation}y = ax^{2} + bx + c\\end{equation}\n",
    "\n",
    "***a***, ***b***, ***c***是系数\n",
    "\n",
    "它产生的抛物线有顶点，或者是最高点，或者是最低点。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def plot_parabola(a, b, c):\n",
    "    vx = (-1*b)/(2*a)              # 顶点\n",
    "    vy = a*vx**2 + b*vx + c\n",
    "\n",
    "    minx = int(vx - 10)            # 范围\n",
    "    maxx = int(vx + 11)\n",
    "    x = np.array(range(minx, maxx))\n",
    "    y = a * x ** 2 + b * x + c\n",
    "    miny = y.min()\n",
    "    maxy = y.max()\n",
    "\n",
    "    plt.plot(x, y, color=\"grey\")    # 画曲线\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('y')\n",
    "    plt.grid()\n",
    "    plt.axhline()\n",
    "    plt.axvline()\n",
    "\n",
    "    sx = [vx, vx]                   # 画中心线\n",
    "    sy = [miny, maxy]\n",
    "    plt.plot(sx, sy, color='magenta')\n",
    "\n",
    "    plt.scatter(vx,vy, color=\"red\") # 画顶点\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_parabola(2, 2, -4)\n",
    "plt.show()\n",
    "plot_parabola(-2, 3, 5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 抛物线的交点（二次方程的解）\n",
    "\n",
    "\\begin{equation}y = 2(x - 1)(x + 2)\\end{equation}\n",
    "\n",
    "\\begin{equation}2(x - 1)(x + 2) = 0\\end{equation}\n",
    "\n",
    "\\begin{equation}x = 1\\end{equation}\n",
    "\n",
    "\\begin{equation}x = -2\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TEzl48CBXrlyxHUcp1YV27NhBcHAwiYmJtqN0OS0QHjJ9+nREhJ07d9qOopTqIuXl5Rw6dIikpCSCg4Ntx+lyWiA8pE+fPkyaNIm9e/dSXV1tO45Sqgvs3Lnz1i2HuyMtEB40c+ZMGhoa2L17t+0oSqlOqqqqoqCggMmTJ9O7d2/bcdxCC4QH3XXXXcTFxZGbm8v169dtx1FKdUJOTg4Oh4OZM2fajuI2WiA8LDU1ldraWvLz821HUUp1UH19Pbm5uYwfP56BAwfajuM2WiA8bNiwYQwfPpxdu3bhcDhsx1FKdcCePXuor6/v1lsPoAXCitTUVK5evcr+/fttR1FK3aEbN26wc+dOYmJiGDJkiO04bqUFwoIxY8YQHR3N1q1b9YZCSvmY3bt3U1VV5ZV3s+tqWiAsEBHS0tK4evUqeXl5tuMopdqprq6Or776itGjRzNixAjbcdxOC4QlsbGxjBw5ku3bt1NfX287jlKqHXbs2EFdXR1paWm2o3iEFgiL0tLSqKmp0aurlfIB165dIycnh/j4eKKiomzH8QgtEBYNGTKEcePGsXPnTr26Wikvt23bNhwOB/PmzbMdxWPcWiBE5B0RuSgiB5qNGyAiX4pIsfOxv3O8iMhvRKRERPaLyFR3ZvMW8+fP58aNG3z11Ve2oyilWnHlyhXy8/OZOnUqAwYMsB3HY9y9BfFHYFGLcT8CMowxY4AM52uAxcAY57AKeM3N2bxCREQEkydPJjc3l6tXr9qOo5RyITMzEz8/P+655x7bUTzKrQXCGLMNuNxi9EPAn5zP/wQ83Gz8n02TXUA/ERnsznze4ubpcllZWVZzKKW+6fz58xQWFjJt2jTCw8Ntx/EoG3e3iDTGnAMwxpwTkUHO8UOA083mO+Mcd675wiKyiqYtDCIjIzv1o1pVVeU1P8qDBw+moKCAgIAAwsLCAO/K54rma11CRQIABVkFLqdXVNTicDi0/TrBU/kKCwsJCAjAGHNH6/P29msPb7r9kasbuZpvjDDmTeBNgKSkJNOZi1WysrK85mKXlJQU/v3f/53q6mqWLFkCeFc+VzTfbfRremht/a8d3klFRYW2Xyd4It+pU6fYunUraWlpzJo1646W9fb2aw8bZzFduLnryPl40Tn+DDCs2XxDgbMezmZNaGgoM2fO5Ouvv6a0tNR2HKV6PGMMmzdvpnfv3kybNs12HCtsFIgNwDPO588AnzQb/7TzbKbpwNWbu6J6iunTpxMaGsrmzZsx5hsbT0opDyouLub06dPMmTOHwMBA23GscPdpru8DO4E4ETkjIs8DrwILRKQYWOB8DZAOHANKgLeA77kzmzcKDg7mnnvu4cSJExw7dsx2HKV6LGMMW7ZsoX///kyZMsV2HGvcegzCGPNkK5O+cZ26afqT+fvuzOMLEhMT2blzJxkZGYwZM8Z2HKV6pAMHDnDhwgUeeeQR/P39bcexRq+k9jIBAQHMnTuXc+fOcenSJdtxlOpxHA4HmZmZREVFMWHCBNtxrNIC4YUmTZrEXXfdxfHjx2lsbLQdR6keJT8/nytXrjB//nxEXJ1c2XNogfBCfn5+zJ8/n9raWgoKXJ9Hr5TqetevX2fbtm2MGDGC0aNH245jnRYILxUXF0d4eDhbt27lxo0btuMo1SPk5ORQVVVFWlpaj996AC0QXktEiI2NpbKyktzcXNtxlOr2amtr2bFjB3fffTfDhg1re4EeQAuEF+vXrx+jRo3iq6++oq6uznYcpbq1r776ivr6eubPn287itfQAuHl0tLSqK2t1ZsKKeVGlZWV7N69m0mTJhEZGWk7jtfQAuHlBg8ezIQJE9i5cydVVVW24yjVLW3bto3Gxkaf7zupq2mB8AHz5s2joaGB7du3246iVLdTXl5Ofn4+iYmJ9O/f33Ycr9JmgRCRF2/e9U3ZMXDgQKZMmUJeXh5XrlyxHUepbiUzM5OAgIAedzOg9mjPFkQUkCsiH4rIItFzv6yYM2cOfn5+bN261XYUpbqNc+fOcfDgQaZPn07v3r1tx/E6bRYIY8xLNN0G9G3gWaBYRP6XiIxyczbVTJ8+fUhJSWHfvn1cvHix7QWUUm3asmULvXr1YubMmbajeKV2HYNwdqR33jk0AP2BdSLySzdmUy3MmjWL4OBgtmzZYjuKUj7vxIkTlJSUMGvWLEJCQmzH8UrtOQbx30VkD/BLYAcw0Rjz34BE4BE351PN9OrVi9TUVA4fPszp06fbXkAp5ZIxhoyMDMLDw0lOTrYdx2u1ZwsiAlhujFlojFlrjLkBYIxpBJa6NZ36hmnTphEWFkZGRobeVEipDjpy5Ahnzpxh7ty5PfZmQO3RnmMQPzXGnGxl2tddH0ndTlBQEHPmzOHkyZMUFxfbjqOUz3E4HGRkZDBw4EASEhJsx/Fqeh2ED5o6dSoRERFs3LhRO/JT6g7t2rWLsrIyFixYgJ+f/gTejraOD/L392fp0qVUVFSwbds223GU8hkVFRVkZWUxduxY4uLibMfxeh4vECISJyIFzYZKEfmBiLwsIqXNxt/v6Wy+ZMSIESQkJJCdna2nvSrVDsYYNm7ciIiwaNEi23F8gscLhDHmsDEmwRiTQNOZUDXAX52T/+3mNGNMuqez+ZoFCxYQHBzM559/rgeslWpDUVERR44cYd68efTt29d2HJ9gexdTGnC0tYPg6vZCQ0NZsGABp06d0jvPKXUb9fX1fPHFF0RGRjJt2jTbcXyG2PzLU0TeAfKNMb8TkZdpulK7EsgD/tEY842Oh0RkFbAKIDIyMnHNmjUdXn9VVZVXX17fnnzGGPbt20d1dTUpKSkePWWvO7SfuyT8oOnsmIJfuy7cP8+pxeFw8NJMbb+OupN8JSUllJaWMmXKFPr06ePmZE28uf3mzZu3xxiT1OaMxhgrAxAEXAIina8jAX+atmpeAd5p6z0SExNNZ2RmZnZqeXdrb74LFy6Yn/3sZ+bjjz92b6AWukv7ucUc59CKx1/PNve9mu6hMB3TXT7fs2fPmn/+5382n376qXsDteDN7QfkmXb8TtvcxbSYpq2HCwDGmAvGGIdpugDvLSDFYjafMmjQIGbMmEFBQQEnTpywHUcpr9HY2Mjnn39OaGgoaWlptuP4HJsF4kng/ZsvRGRws2nLgAMeT+TD5syZQ79+/fj8889xOBy24yjlFfbs2UNpaSn33XcfvXr1sh3H51gpECISCiwAPmo2+pciUigi+4F5wD/YyOarAgMDuf/++7l06RLZ2dm24yhlXVVVFRkZGYwcOZKJEyfajuOTAmys1BhTAwxsMW6ljSzdyZgxYxg/fjzbtm0jPj5e746lerRNmzbR0NDAkiVL0NvYdIzt01xVF1u4cCF+fn6kp6frtRGqxzp69CgHDhxg1qxZDBw4sO0FlEtaILqZPn36MG/ePEpKSjh06JDtOEp5XENDA+np6QwYMIBZs2bZjuPTtEB0QykpKQwePJgvvviC+vp623GU8qjt27dz+fJllixZQkCAlb3o3YYWiG7Iz8+PJUuWUFVVpXefUz3KpUuX2LFjBxMnTiQ2NtZ2HJ+nBaKbGjJkCMnJyeTm5nL27FnbcZRyO2MM6enpBAYGct9999mO0y1ogejG5s+fT1hYGJ999hmNjY224yjlVoWFhRw/fpy0tDSv7eLC12iB6MZCQkJYtGgR586dIzc313YcpdymtraWTZs2MXToUBITE23H6Ta0QHRz48ePZ9SoUWzZsoVr167ZjqOUW2zevJna2lq95qGLaYHo5kSE+++/n8bGRr744gvbcZTqcqdPnyY/P5/p06cTFRVlO063ogWiBxgwYACzZ8/m0KFDFBcX246jVJdxOBx89tln9OnTh7lz59qO0+1ogeghZs6cSUREBOnp6dy4ccN2HKW6RE5ODhcvXmTx4sUEBQXZjtPtaIHoIQICAliyZAkVFRVs27bNdhylOq2uro6srCzi4uIYO3as7TjdkhaIHiQmJobJkyeTnZ1NWVmZ7ThKdUpJSQkAixYtspyk+9IC0cMsWLCA4OBgPvvsM+3MT/msoqIiysvLmTt3Lv369bMdp9vSAtHDhIWFce+993Lq1Cny8vJsx1HqjtXU1JCenk5YWBjTpk2zHadb0wLRA02ZMoXRo0ezadMmLly4YDuOUu1mjOGTTz6hpqaGuLg4/P39bUfq1rRA9EAiwsMPP0xoaChr167l+vXrtiMp1S45OTkcOXKEBQsWEB4ebjtOt6cFoocKCwtj+fLlXL58mfT0dNtxlGpTaWkpX375JWPHjiUlJcV2nB7BWoEQkRPOe1AXiEiec9wAEflSRIqdj3rPTDeKiYlhzpw57Nu3j4KCAttxlGpVXV0d69atIzw8nAcffFC70/AQ21sQ84wxCcaYJOfrHwEZxpgxQIbztXKj2bNnExMTQ3p6up76qrySMYZPP/2UyspKHn30UXr16mU7Uo9hu0C09BDwJ+fzPwEPW8zSI/j5+bF8+XICAwNZt26dXmWtvE5eXh6HDh1i/vz5DB061HacHkVsnQsvIseBK4AB3jDGvCkiFcaYfs3muWKM6d9iuVXAKoDIyMjENWvWdDhDVVWVV/cb78l8ly9fprCwkMGDB3P33Xe3axltv9Yl/CABgIJfu9519/OcWhwOBy/N1PZrK0N+fj79+/cnPj7+73YteUO+2/HmfPPmzdvTbM9N64wxVgYg2vk4CNgH3ANUtJjnyu3eIzEx0XRGZmZmp5Z3N0/n27x5s3n55ZdNYWFhu+bX9ruNOc6hFY+/nm3uezXdQ2E6xvbnW1dXZ37729+aX/3qV6aqquob023na4s35wPyTDt+p63tYjLGnHU+XgT+CqQAF0RkMIDz8aKtfD3RvHnzGDZsGJ9++imXL1+2HUf1YMYYPv/8cy5fvszy5csJCwuzHalHslIgRCRMRMJvPgfuAw4AG4BnnLM9A3xiI19P5efnxyOPPIK/vz9r166loaHBdiTVQxUUFFBYWMicOXOIiYmxHafHsrUFEQl8JSL7gN3A58aYL4BXgQUiUgwscL5WHtS3b18eeughzp8/z5dffmk7juqBysrKSE9PZ+TIkcyePdt2nB4twMZKjTHHgMkuxpcDaZ5PpJqLi4tj+vTp7Nq1i5iYGMaNG2c7kuohbty4wdq1awkODmbZsmX4+XnbiZY9i7a+cunee+8lOjqaDRs2UFFRYTuO6iE2btxIWVkZy5Yt0640vIAWCOWSv78/jz76KMYY1q1bh8PhsB1JdXOFhYXs3buX2bNnM2rUKNtxFFog1G3079+fBx54gNLSUrZs2WI7jurGysvL+eyzzxg+fLjeW9qLaIFQtzVhwgSSkpLIzs6muLjYdhzVDTU0NLBu3Tr8/f155JFH9LiDF9FPQrVp4cKFREZG8te//pXKykrbcVQ387e//Y3z58/z8MMP06dPH9txVDNaIFSbAgICePTRR2loaGD9+vU0NjbajqS6iUOHDpGbm8uMGTPa3cWL8hwtEKpdIiIiWLp0KadOnWLr1q2246hu4MqVK2zYsIEhQ4aQlqZnt3sjK9dBKN80adIkjh8/zrZt2xgxYoTtOMqHORwO1q9fD3Dr6n3lfXQLQt2RxYsXExERwUcffaS3KlUdtnnzZkpLS3nwwQfp31/vC+attECoOxIUFMRjjz3G9evXKSwspK6uznYk5WNycnLYtWsXycnJjB8/3nYcdRtaINQdGzRoEI8//jjV1dW8//77epMh1W779+/niy++YOzYsSxatMh2HNUGLRCqQ0aPHs3YsWM5deoUa9eu1SutVZsOHz7Mxx9/TExMjF7v4CP0E1IdNmjQIJYuXUpxcTGffPLJzZs8KfUNJ0+eZN26dQwePJgnnniCgAA9P8YX6KekOiUxMZHa2loyMjIICQlh8eLFf3dbSKXOnTvH+++/T79+/XjqqacIDg62HUm1kxYI1WmpqanU1taSnZ1Nr169mDdvnu1IykuUl5fz3nvvERISwsqVKwkNDbUdSd0BLRCq00SEe++9l9raWrZt20avXr2YPn267VjKsqtXr/Luu+8CsHLlSu1GwwdpgVBdQkRYunQpdXV1bNq0iZCQEBISEmzHUpZUV1fz3nvvUVdXxzPPPMPRlHx8AAASiUlEQVTAgQNtR1Id4PGD1CIyTEQyReRrETkoIv/DOf5lESkVkQLncL+ns6nO8fPzY/ny5cTGxrJhwwaKiopsR1IW1NfXs3r1aioqKnjyyScZPHiw7Uiqg2ycxdQA/KMxZhwwHfi+iNy8WubfjDEJziHdQjbVSQEBAaxYsYLo6GjWrVvH8ePHbUdSHtTQ0MCaNWu4cOECjz32mHbJ4uM8XiCMMeeMMfnO59eAr4Ehns6h3CcoKIhvfetbDBgwgDVr1nD27FnbkZQHNDY2sm7dOk6cOMHDDz+svbN2A1avgxCRGGAKkOMc9aKI7BeRd0REO2jxYaGhobfOWnnvvfcoKyuzHUm5kTGGDRs2cPjwYRYvXszEiRNtR1JdQGxd3CQivYGtwCvGmI9EJBK4BBjgX4DBxpjnXCy3ClgFEBkZmbhmzZoOZ6iqqqJ3794dXt7dukO+2tpa9u7di5+fHwkJCYSEhHgond32S/hB0wH6gl8XuJz+85xaHA4HL8307c8XmorD0aNHKS0tJSYmxmO7lbrD/w9b5s2bt8cYk9TmjMYYjw9AILAJ+J+tTI8BDrT1PomJiaYzMjMzO7W8u3WXfOfPnzevvvqq+c1vfmOqqqrcG6oZq+03xzm04vHXs819r6Z7KEzHtLf9srKyzMsvv2w2btxoGhsb3Ruqme7y/8MGIM+047faxllMArwNfG2M+d/Nxjc/1WEZcMDT2ZR7REZG8uSTT1JZWXnr1EfVPezevZusrCwmT57MwoUL9Sr6bsbGMYhUYCUwv8Uprb8UkUIR2Q/MA/7BQjblJsOHD2fFihVcvHhRe4DtJvbv38/GjRuJi4vjwQcf1OLQDXn8QjljzFeAq2+SntbazY0ePZply5axfv161q5dy4oVK/ROYj7qyJEjt3pmffTRR7Vn1m5KP1XlUfHx8SxZsoTi4mJWr15NTU2N7UjqDuXn5/Phhx8SFRWlPbN2c1oglMclJSXx0EMPcerUKd566y0uXLhgO5JqB4fDweeff86nn37KiBEjWLlypfbM2s1pgVBWJCQk8Oyzz+JwOHj77bc5dOiQ7UjqNqqrq3n33XfJy8tjxowZPPXUU/Tq1ct2LOVmWiCUNUOHDuW73/0ukZGRrF27li1btuhNh7zQuXPnePPNNyktLWXZsmXcd999esyhh9BPWVkVHh7OM888w5QpU9i+fTtr1qzR02C9SGFhIe+88w4A3/nOd5g0aZLlRMqTtEAo6wICAnjggQe4//77KSkp4Q9/+AOXLl2yHatHa2xs5OjRo3z00UdER0ezatUqoqOjbcdSHqYFQnkFESE5OZmVK1dSW1vLH/7wB44cOWI7Vo9UW1vLX/7yF86cOUNSUhJPP/00YWFhtmMpC7RAKK8SExPDqlWr6N+/P++//z7bt2/X4xIedPHiRd566y2OHz/O3XffzZIlS/RalR5MC4TyOn379uW5554jPj6eLVu2sG7dOq5fv247VrdXVFTE22+/zfXr13nmmWf0Rj9KbzmqvFNgYCDLly8nKiqKjIwMysvLWbFiBf37ay/wXc0Yw9atW9m6dSvR0dGsWLGCPn36cOzYMdvRlGW6BaG8loiQmprKt771La5evXpr14fqOvX19Xz44Yds3bqVyZMn853vfIc+ffrYjqW8hBYI5fVGjx7Nd7/7XXr37s27777Lrl279LhEF7h8+TJvv/02hw8fZuHChTz00EPabYb6O1oglE8YMGAAzz//PHFxcWzatIlPPvlEe4TthOLiYt566y2qqqr49re/zfTp07U3VvUN+ueC8hnBwcE8/vjjt/aXHzt2jLlz55KQkKBX9rZTWVkZGRkZHD58mMjISD2uo25L/1cpnyIizJ07l2effZa+ffvy6aef8tprr1FUVNRlu50WLVpEv379WLp0aZe8nycVFBQwY8YMJkyYwKRJk/jggw8AqKysZMOGDbz22mscP36cefPm8fzzz2txULelWxDKJ40YMYLnnnuOoqIiMjIy+OCDDxg2bBj33nsvw4cP79R7/9M//RM1NTW88cYbXZTWc0JDQ/nzn//MmDFjOHv2LFOnTiU4OJiDBw/S2NhISkoK99xzD6GhobajKh+gWxDKZ4kI48aN43vf+x5Lly7lypUr/Od//idr1qzh4sWLbS6fm5vLpEmTqKuro7q6mgkTJnDgwAHS0tIIDw/3wL+gc1zlv379OmPGjKGhoYETJ04gImzZsoXx48fz4osvsmjRIi0Oqt10C0L5PD8/PxITE5k0aRK7du1ix44dvP7660RGRjJlyhT69u3rcrnk5GQefPBBXnrpJWpra/n2t79NfHy8h9N3nKv848ePp6CggMzMTA4dOoSfnx8/+tGPtB8l1SFeVyBEZBHw74A/8AdjzKuWIykfERgYyOzZs0lMTGT79u3k5OTw29/+lmnTpjFr1iyX9y/46U9/SnJyMiEhIfzmN7+xkLpzmuf//ve/z+uvv05ZWRmhoaFkZGSwfv16LQ6qw7yqQIiIP/AfwALgDJArIhuMMXo3GdVuoaGhLFy4EGMMdXV1ZGdnk5+fz6xZs0hJSeHDog/5ScZPOHX1FENkCNcvX2dg+EDq6up8olO61YWr/y5//aV6AkwAq1evJioqisWLF/PCCy/wi1/8gunTp9uOq3yYVxUIIAUoMcYcAxCRNcBDgBYIdcdCQkJYtGgRM2bMICMjg82bN5P5VSaf3fiM047TGAxnVp8haGYQcwbN4Yc//CG/+93vbMe+rdWFq1n16SpqbtQQQQSNqxuZPX02V6uuUlxczEsvvcTSpUt5+umneeyxx2zHVT5OvOmKVBF5FFhkjPk/nK9XAtOMMS+6mn/AiHFmwf/7TofXV1FRQb9+/Tq8vLtpvs5pma+uro7TF04TRBDXuc7Zwgwqj+TT55GnCJZAqv7yDhMffoGDn73NtfMnaaivISisL8krf0zUhDv7S/ynvxoPwM/+0fXfNofOVdLQ0MCkYQPu6H13n9mNOIRQQqkt3MPlI3kMeuQ56qSWqr+8zei5j5D75/9F3+jYW8skP/MT+g+7+47WA773+Xobb8734Qsz9xhjktqaz9sKxGPAwhYFIsUY8381m2cVsAogNHJk4qx/+I8Or8/hcHh1V8aar3Nc5bt2/Ro4oPFGIzT76ou/EBIUQmBgACKdP7nvl2+kAPD//J+7XU4/da0RYwwj+rTdfg0NDbcGh8PxX5kDpGlwXgHdO6h3p3M354ufrzfx5nx/+9H9PlkgZgAvG2MWOl//GMAY83NX8yclJZm8vLwOry8rK4u5c+d2eHl303yd4ypfzK9jOHn1JAB96EMssYxiFKNlNL1M00Hsu+66i9jYWGJjY4mJiSEoKOjOV35ztVmuJ694YycVFRVs+uHivxtvjKGsrIyjR49y7NgxTp48yY0bNxARhg4dyoaLG8ivz6eUUhppvLXciL4jOPGDE3ee8zZ88fP1Jt6cT0TaVSC87RhELjBGREYCpcATwLfsRlLdyStpr9zah19JJQUUcCTwCG8sfYN7B93L0aNHOX78OHv27CEnJwc/Pz+GDRt2q2BER0e33a3H6tWwaxTU10HMs/DKK/DUU63Ofu3aNY4dO3ZrqKqqAmDgwIEkJCQwatQoYmJiCA4OJrgwmC8//bJpC8gpNDCUV9Je6YrmUerveFWBMMY0iMiLwCaaTnN9xxhz0HIs1Y08NbHph/rmWUDD+w7nlbRXbo2PiooiNTWVhoYGTp06detHOzMzk8zMTEJCQoiJiSE2NpbevV3s0tm2DV57jeH+b0JoKKdCQ+Ff/xWqquCee27NVl1dTW1tLb///e8pKysDms6+ulmIYmNjXV6/0VZ+pbqSVxUIAGNMOpBuO4fqvp6a+FSbP6gBAQG3fqgBampq/u6v/KKiotYXXraMhRub/sLftHhF07jz5+HDD2/Ncqk+DoDw8HAmT55MbGwsUVFR7epRtT35leoKXlcglPJGoaGhxMfHEx8fjzGGiooK17dBnTzZ+eQ1AF54rdm0ffv+6+naIqqrq1m58n73hVaqk7RAKHWHRKT1XlBDQuDkyW+OHzECIiNvvQwMPAbUuCegUl1EO+tTqiu98gq07AwvNLRpvFI+RguEUl3pqafgzTebthhEmh7ffPO2ZzEp5a10F5NSXe2pp7QgqG5BtyCUUkq5pAVCKaWUS1oglFJKuaQFQimllEtaIJRSSrmkBUIppZRLWiCUUkq5pAVCKaWUS151w6A7JSJlgIuOb9otArjURXHcQfN1jubrHM3XOd6cb4Qx5q62ZvLpAtFZIpLXnrsq2aL5OkfzdY7m6xxvz9ceuotJKaWUS1oglFJKudTTC8SbtgO0QfN1jubrHM3XOd6er009+hiEUkqp1vX0LQillFKt6NYFQkQeE5GDItIoIkktpv1YREpE5LCILGxl+ZEikiMixSLygYgEuTnvByJS4BxOiEhBK/OdEJFC53x57szUYr0vi0hps4wub6gsIouc7VoiIj/yYL5/FZEiEdkvIn8VkX6tzOex9murLUQk2Pm5lzi/azHuzONi/cNEJFNEvnb+X/kfLuaZKyJXm33uP/Vwxtt+XtLkN8423C8iUz2YLa5ZuxSISKWI/KDFPFbbr1OMMd12AMYBcUAWkNRs/HhgHxAMjASOAv4ulv8QeML5/HXgv3kw+6+An7Yy7QQQYaE9Xwb+7zbm8Xe2ZywQ5Gzn8R7Kdx8Q4Hz+C+AXNtuvPW0BfA943fn8CeADD3+mg4GpzufhwBEXGecCn3n6+9bezwu4H9gICDAdyLGU0x84T9M1Bl7Tfp0ZuvUWhDHma2PMYReTHgLWGGPqjTHHgRIgpfkMIiLAfGCdc9SfgIfdmbfFuh8H3vfE+rpYClBijDlmjLkOrKGpvd3OGPM3Y0yD8+UuYKgn1nsb7WmLh2j6bkHTdy3N+fl7hDHmnDEm3/n8GvA1MMRT6+8iDwF/Nk12Af1EZLCFHGnAUWNMZy7e9SrdukDcxhDgdLPXZ/jmf4qBQEWzHxxX87jLbOCCMaa4lekG+JuI7BGRVR7KdNOLzs34d0Skv4vp7WlbT3iOpr8qXfFU+7WnLW7N4/yuXaXpu+dxzt1bU4AcF5NniMg+EdkoIhM8Gqztz8tbvnNP0PofdTbbr8N8/p7UIrIZiHIx6SfGmE9aW8zFuJanc7VnnjvWzrxPcvuth1RjzFkRGQR8KSJFxphtnc3WVj7gNeBfaGqHf6FpN9hzLd/CxbJddqpce9pPRH4CNACrW3kbt7Vfy7guxnnke3anRKQ3sB74gTGmssXkfJp2m1Q5jzt9DIzxYLy2Pi/rbeg8Pvkg8GMXk223X4f5fIEwxtzbgcXOAMOavR4KnG0xzyWaNlUDnH/ZuZrnjrWVV0QCgOVA4m3e46zz8aKI/JWmXRld8gPX3vYUkbeAz1xMak/bdlg72u8ZYCmQZpw7gF28h9var4X2tMXNec44P/u+wGU3ZGmViATSVBxWG2M+ajm9ecEwxqSLyO9FJMIY45F+htrxebn1O9dOi4F8Y8yFlhNst19n9NRdTBuAJ5xnkIykqZrvbj6D88clE3jUOeoZoLUtkq50L1BkjDnjaqKIhIlI+M3nNB2YPeCBXLTYr7uslfXmAmOk6QywIJo2uzd4KN8i4IfAg8aYmlbm8WT7tactNtD03YKm79qW1gqbOziPd7wNfG2M+d+tzBN187iIiKTQ9LtR7qF87fm8NgBPO89mmg5cNcac80S+Zlrd6rfZfp1m+yi5OweafsTOAPXABWBTs2k/oekMk8PA4mbj04Fo5/NYmgpHCbAWCPZA5j8CL7QYFw2kN8u0zzkcpGnXiqfa812gENhP03/KwS3zOV/fT9PZMEc9nK+Epn3RBc7h9Zb5PN1+rtoC+BlNRQwgxPndKnF+12I91V7O9c+iaXfM/mbtdj/wws3vIfCis6320XTwf6YH87n8vFrkE+A/nG1cSLMzFj2UMZSmH/y+zcZ5Rft1dtArqZVSSrnUU3cxKaWUaoMWCKWUUi5pgVBKKeWSFgillFIuaYFQSinlkhYIpZRSLmmBUEop5ZIWCKW6kIgkOzszDHFeBXxQROJt51KqI/RCOaW6mIj8fzRdId0LOGOM+bnlSEp1iBYIpbqYs9+lXKCOpm4VHJYjKdUhuotJqa43AOhN0x3aQixnUarDdAtCqS4mIhtounvcSJo6NHzRciSlOsTn7wehlDcRkaeBBmPMX0TEH8gWkfnGmC22syl1p3QLQimllEt6DEIppZRLWiCUUkq5pAVCKaWUS1oglFJKuaQFQimllEtaIJRSSrmkBUIppZRLWiCUUkq59P8D6nrnYV7jCkMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 画曲线\n",
    "plot_parabola(2, 2, -4)\n",
    "\n",
    "# 画交点\n",
    "x1 = -2\n",
    "x2 = 1\n",
    "plt.scatter([x1,x2],[0,0], color=\"green\")\n",
    "plt.annotate('x1',(x1, 0))\n",
    "plt.annotate('x2',(x2, 0))\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 二次方程的解公式\n",
    "\\begin{equation}ax^{2} + bx + c = 0\\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}x = \\frac{-b \\pm \\sqrt{b^{2} - 4ac}}{2a}\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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oiBSKSJ9ZIwkJCYiIXsxRqT7o4sWLHDp0iLi4OAICAmzH8SpvbZG8Ciy/ZtizwC5jTBSwy/0YYAXNfbVHAeuBl7yU0eMGDx5MTEwM+fn5VFdX33wCpVSvkZGRga+vL/PmzbMdxeu8UkiMMbuBa/tevx/4k/v+n4BVrYa/ZpplAqEiEuGNnN6QmJhIY2Mje/futR1FKdVDKisrKSgo4LbbbiM4ONh2HK/zeJ/tNxBujDkDYIw5IyIj3MNHA637qS11DzvTemIRWU/zFgvh4eGkpaV5PHBbKisrOz3vYcOGsWfPHlwul8ca5LqSy9PKy2twuVyOywWeW16zyps7MipIK+jS9E5cj6C5rvXll19e/Ty3NX+nLq+eYrOQtKetA6+vOyXcGPMy8DJAXFycSUpK8nCstqWlpdHZeUdGRvLqq68yZMgQ4uPjHZPL0146kkF5ebnjcoEHl1do85+uvrYT1yNortbq6+vJysri1ltvZeXKlY7J5U02j9r6umWXlfvvOffwUmBsq/HGAH3q5Itx48YxZswYPv/8cxobG23HUUp1Q3Z2NrW1tf3mcihtsVlItgKPu+8/DrzXavhj7qO3EoDLLbvA+goRITk5mYqKCnJzc23HUUp1UW1tLXv27GHy5MmMHTv25hP0Ud46/HcTkAFMFZFSEXkS+AVwp4gUA3e6HwNsB44DR4H/BH7kjYzeFhkZyYQJE/jss8+or6+3HUcp1QUZGRnU1NSwZMkS21Gs8kobiTHmkXaeWtrGuAb4a88msk9EWLJkCRs2bGDv3r0sXLjQdiSlVCdUV1eTmZnJtGnTiIjoMweWdome2W7R2LFjiYqKYs+ePdTW1tqOo5TqhM8//5yGhgaSk5NtR7FOC4llS5Ysoba2Vq/BpVQvcuXKFbKzs4mJieGWW26xHcc6LSSWjRw5kujoaDIzM6mqqrIdRynVAbt376apqYnbb7/ddhRH0ELiAElJSTQ2NvL555/bjqKUuomysjLy8vKYM2cOYWFhtuM4ghYSBxg+fDi33XYb2dnZVFRU2I6jlLqBTz/9FB8fHxYvXmw7imNoIXGI22+/HWMMu3fvth1FKdWO8+fPU1hYSHx8PIMHD7YdxzG0kDhEaGgosbGx5Ofnc+nStde3VEo5QWpqKv7+/nq4/jW0kDjIokWL8PHx4dNPP7UdRSl1jdOnT3Po0CHmz59PYGCg7TiOooXEQQYPHszcuXMpLCzk3LlzN59AKeU1qampDBo0iPnz59uO4jhaSBxmwYIFBAQEkJqaajuKUsrtq6++4ujRo1c/n+rbtJA4TGBgIPPnz+fw4cOcOnXKdhyl+j1jDLt27SI4OJi5c+fajuNIWkgcKCEhgUGDBulWiVIOcOzYMb766isWLVqEv7+/7TiOpIXEgQICAli4cCHHjh3j5MmTtuMo1W8ZY0hNTSUkJITY2FjbcRxLC4lDtRyn/sknn9B8QWSllLcdPnyY06dPk5SU5LFusfsCLSQO5e/vz6JFi6428imlvKupqYnU1FSGDRtGTEyM7TiOZq2QiMhUESlodasQkadF5HkROdVqeNudIPcDc+bMITQ0VLdKlLJg//79nD9/nuTkZHx89Df3jVhbOsaYI8aYWcaYWUAsUA284376Vy3PGWO228pom6+vL0lJSZw9e5ZDhw7ZjqNUv+FyuUhLS2PkyJFMnz7ddhzHc0qZXQocM8Zoy/I1Zs6cyfDhw0lNTaWpqcl2HKX6hfz8fMrKykhOTkZEbMdxPKcUkoeBTa0e/1hECkVkg4j06+s0+/j4kJyczIULFygqKrIdR6k+r6Ghgd27d1/twVTdnNje9y4iA4DTQLQx5msRCQcuAAb4RyDCGPODNqZbD6wHCA8Pj928ebMXU3+jsrKS4OBgj87DGENeXh6NjY3Ex8d3aH+tN3J11s+zanC5XDyX6Kxc4LnlNevpWQAU/LqgS9M7cT1C385VUlLC8ePHue222wgNDXVMLk9ITk7ONcbEdfuFjDFWb8D9wM52npsA7L/Za8TGxhpbUlNTvTKf4uJi8/zzz5u9e/d2aHxv5eqMh36fbu76xXbbMdrkseV1u/vWRU5cj8b03Vy1tbXmxRdfNK+99lrPBHJz6vICckwPfI87YdfWI7TarSUiEa2eWw3s93oiB5o0aRLjxo1j9+7dNDQ02I6jVJ+UlZVFdXU1S5YssR2lV7FaSEQkELgTeLvV4BdFpEhECoFk4G+thHMYEWHJkiVUVlaSnZ1tO45SfU5NTQ3p6elMnTqV0aNH247Tq9y0kIjIjz3V4G2MqTbGDDPGXG417HvGmJnGmBhjzH3GmDOemHdvNH78eCZNmsTnn39OXV2d7ThK9Sl79uyhrq6O5ORk21F6nY5skYwEskXkTRFZLnosnFVLliyhpqaGjIwM21GU6jMqKyvJyspi5syZhIeH247T69y0kBhjngOigD8CTwDFIvLPIjLJw9lUG0aNGsW0adPIyMjgypUrtuMo1SekpqbicrlISkqyHaVX6lAbibt1/6z71giEAW+JyIsezKbacccdd+ByuUhJSbEdRale79SpU+Tl5TFv3jyGDh1qO06v1JE2kv8lIrnAi8AeYKYx5q9ovqzJdzycT7Vh6NChLFiwgKKiIk6cOGE7jlK9VlNTE9u3byc4OFi3RrqhI1skw4E1xphlxpi/GGMaAIwxTcA9Hk2n2rVw4UJCQ0PZvn07LpfLdhyleqX8/HxOnz7NXXfdpV3odkNH2kh+Ztq5BpYxRq8kaIm/vz/Lly/n/Pnz7N2713YcpXqd6upqdu3axfjx45kxY4btOL2aE05IVF00ZcoUoqKiSEtL04Z3pTpp165d1NbWsnLlSr0wYzdpIenFRITly5fjcrnYuXOn7ThK9RqlpaXk5eWRkJDAiBEjbMfp9bSQ9HJDhw5l4cKF7N+/ny+//NJ2HKUcr6WBffDgwdx+++224/QJWkj6gAULFhAaGsqOHTu04V2pm8jLy+PMmTPawN6DtJD0Af7+/qxYsYLz58+TlZVlO45SjtXSwD5hwgSio6Ntx+kztJD0EVOmTGHKlCl8+umnVFRU2I6jlCN9/PHH1NfXawN7D9NC0oe0NLzrGe9KXa+0tJT8/HzmzZvHLbfcYjtOn6KFpA8JCwu72vBeVlZmO45SjqEN7J6lhaSPWbBgAWFhYRw9elQb3pVyy83N1QZ2D7JeSETkhLsjqwIRyXEPGyoiKSJS7P7rkf5Q+qKWM96rq6vJzMy0HUcp66qqqvjkk0+IjIzUBnYPsV5I3JKNMbPMN53QPwvsMsZEAbvcj1UHTZkyhWHDhmnDu1J808C+YsUKbWD3EKcUkmvdD/zJff9PwCqLWXqlSZMmYYzRM95Vv1ZSUkJBQQEJCQnawO5BTigkBtgpIrkist49LLyli133X72GQScNGjSIhQsXcuDAAY4fP247jlJepw3s3iPNfVZZDCAyyhhzWkRGACnA3wBbjTGhrcYpM8aEXTPdemA9QHh4eOzmzZu9GfuqyspKgoODrcz7RiorKwkMDCQ7OxsfHx9iY2Px8bH7u+HnWTW4XC6eS3Tm8vLEepz19CwACn5d0KXpnfz+cnquU6dOcfToUaZPn259a8Spyys5OTm3VZNCl/n1RJjuMMacdv89JyLvAHOBr0UkwhhzRkQigHNtTPcy8DJAXFycsdUpTVpamiM7xGnJNXbsWF5//XUCAgJYsGCB1UwvHcmgvLzc0curx7l/DnX1tZ3+/nKallxVVVVkZWUxceJEHnjgAettI05dXj3F6k9UEQkSkcEt94G7gP3AVuBx92iPA+/ZSdj7RUVFceutt/Lpp59y+fJl23GU8gptYPcu220k4cDnIrIP2At8YIz5EPgFcKeIFAN3uh+rLlq2bJk2vKt+o6WBff78+QwfPtx2nH7B6q4tY8xx4LY2hl8Elno/Ud8UGhrKokWLSE1N5dixY0yaNMl2JKU8whjD9u3bGTJkCIsXL7Ydp9+wvUWivCQxMZGhQ4eyY8cOGhsbbcdRyiNOnz7N2bNnWbZsGQMGDLAdp9/QQtJP+Pn5sWLFCi5evKhnvKs+qbKyki+//JKJEycybdo023H6FS0k/cjkyZO59dZb2b17t17UUfU5O3fupKmpSRvYLdBC0s8sX74cHx8f3n77bZqammzHUapH7N+/n6KiIsaNG6cN7BZoIelnQkJCuOeeeygtLWX37t224yjVbZcvX+b9999nzJgxjB8/3nacfkkLST80Y8YMYmJi2L17NyUlJbbjKNVlTU1NvPPOOxhjWLNmje7SskQLST+1cuVKQkJCePvtt6mrq7MdR6ku2bNnDydPnmTlypWEhWlvE7ZoIemnAgICWLNmDZcvX2bHjh224yjVaadPnyYtLY3o6GhiYmJsx+nXtJD0Y2PHjmXx4sXs27eP/fv3246jVIfV19ezZcsWgoODufvuu3WXlmVaSPq5xYsXM2bMGD744AO9FpfqNT766CMuXbrE6tWrGTRokO04/Z4Wkn7Ox8eHNWvWXG201EOCldMdOnSIvLw8Fi5cyIQJE2zHUWghUUBYWBgrV67k5MmTpKen246jVLuuXLnCtm3bGDVqVJ++LHtvo4VEARATE0N0dDSpqamcPn3adhylrmOM4d1336WxsZE1a9bg6+trO5Jy00KiABAR7r77boKDg9myZQv19fW2Iyn1LZmZmRw/fpzly5czbNgw23FUK1pI1FWDBg1i9erVXLp0iY8++sh2HKWuOnv2LLt27eLWW29l9uzZtuOoa2ghUd8yYcIEFixYQF5eHocOHbIdRykaGhrYsmULgwYN4t5779VDfR3IWiERkbEikioih0TkgIj8b/fw50XklIgUuG8rbWXsr5KTk4mIiGDbtm1cuXLFdhzVz6WkpHDhwgVWrVpFYGCg7TiqDTa3SBqBvzPGTAMSgL8Wkenu535ljJnlvm23F7F/8vX1Zc2aNTQ2NvLuu+9ijLEdSfVTX3zxBdnZ2SQkJGjPng5mrZAYY84YY/Lc968Ah4DRtvKobxs+fDjLli3j+PHj2hGWsqKyspKtW7cSHh7O0qXa87aTiRN+bYrIBGA3MAP4P8ATQAWQQ/NWy3W9MInIemA9QHh4eOzmzZu9lPbbKisrCQ4OtjLvG+mJXMYYDhw4wKVLl5gzZ063X+/nWTW4XC6eS+yby6sts56eBUDBrwu6NH1ffn/diDGG/fv3U15ezpw5cwgKCnJErq5yaq7k5ORcY0xct1/IGGP1BgQDucAa9+NwwJfmraUXgA03e43Y2FhjS2pqqrV530hP5aqqqjL/+q//an7729+a+vr6br3WQ79PN3f9YnuP5OppHluPt7tvXdTX31/tycrKMs8//7zJysrq1HT9dXl1FZBjeuB73OpRWyLiD2wBNhpj3gYwxnxtjHEZY5qA/wTm2szY3wUGBrJq1SrOnz9PSkqK7TiqHzh37hwpKSlERUURHx9vO47qAJtHbQnwR+CQMebfWw2PaDXaakAvS2vZpEmTSEhIIDs7m+LiYttxVB/W2NjI22+/TUBAAPfdd58e6ttL2NwiWQB8D1hyzaG+L4pIkYgUAsnA31rMqNyWLl1KeHg47733HpWVlbbjqD5q165dfP3119x///2ObFNQbbN51NbnxhgxxsSYVof6GmO+Z4yZ6R5+nzHmjK2M6ht+fn6sWbOGuro6Nm/eTENDg+1Iqo8pKCggMzOT+Ph4oqKibMdRnaBntqsOGzFiBGvWrOHUqVO8/fbbesl51WOOHz/Otm3bmDhxIsuWLbMdR3WSFhLVKdOmTWPZsmUcPnxYG99Vjzh37hxvvvkmw4cP58EHH9Sr+vZCfrYDqN4nISGBsrIyMjMzCQsLY+5cPbBOdc2VK1d4/fXX8ff3Z+3atQwcONB2JNUFWkhUlyxbtozLly/z4YcfEhISwtSpU21HUr1MfX09mzZtorq6mu9///uEhITYjqS6SHdtqS5p6aI3IiKCLVu2aGdYqlOampp46623OHv2LA8++CARERE3n0g5lhYS1WUDBgzgkUceISgoiNdff53y8nLbkVQvYIxhx44dFBcXs3LlSj1Cqw/QQqK6JTg4mLVr1+Jyudi4cSO1tbW2IymHy8gd1yiqAAATvklEQVTIICcnh8TEROLiun+ZJ2WfFhLVbbfccgsPPfQQly5d4o033sDlctmOpBzq4MGDpKSkMH36dO644w7bcVQP0UKiekRkZCT3338/J06cYOvWrdqHibpOSUkJ77zzDmPHjmXVqlV6+ZM+RI/aUj0mJiaGsrIy0tLSCAsLIykpyXYk5RCXLl1i8+bNDBkyhIcffhh/f3/bkVQP0kKietTixYspLy/n008/JTQ0lFmzZtmOpCyrrq5m48aNGGNYu3atdpfbB+muLdWjRIR77rmHiRMnsm3bNo4fP97haQsKCpg/fz7R0dHExMTwxhtveDCp8obGxkY2b97Mb37zG1544QUef/xx25GUB2ghUT3O19eXBx98kGHDhvHmm29y7ty5Dk0XGBjIa6+9xoEDB/jwww95+umn9ZDiXswYw7vvvktJSQnPPvssf/7zn21HUh6ihUR5xMCBA1m3bh3+/v68/vrrXLly5VvPZ2dnExMTQ21tLVVVVURHR1NfX3/1nIJRo0YxYsQIzp8/byO+6qLW6/X999/nRz/6ERMnTuTJJ59k8ODBtuMpD9E2EuUxISEhrF27lldeeYVNmzZhzIyrz8XHx3Pffffx3HPPUVNTw6OPPsqMGd88v3fvXurr65k0aZKN6KqLWtbrD3/4Q44cOcKKFSt49NFHbcdSHubYLRIRWS4iR0TkqIg8azuP6pqIiAgeeOABzp49e93Wxc9+9jNSUlLIycnh7//+768OP3PmDN/73vd45ZVX8PFx7FtUteORRx4hJSWFS5cu8V//9V96mG8/4MgtEhHxBX4L3AmUAtkistUYc9BuMtUVU6ZMYcWKFWx/5xgNDQ1E/iqSkxUnGS2jqb9Uz7DBw6itrSUoKIiKigruvvtu/umf/omEhATb0VUHbSzayE93/RS5LNx/5X4aGhvw9/envr5eD/XtB5z6c28ucNQYc9wYUw9sBu63nEl1Q3x8PH6BfjQ2NrKgYgF++FG6sZTyxHJmLJ3BM888Q319PatXr+axxx7jwQcftB1ZddDGoo2s37ae4MvBPMqjvLftPRqXNDLzjpk888wztuMpLxAnnoEsIg8Ay40x/8P9+HvAPGPMj9saf+j4aebO/2eDNyNeVV5eTmhoqJV534gTc2WdKGUAAYRJFWeLUvn6i3RCv/MoAeJP5esbmJz0HbJf+2dCRk28Ok384z8lbOwUj2fz1PL62b9NB+Af/q5rG9NOXI/w7VxZpZn4uwYwlKGcKfqEc19kfGu9zlz1FAfe/yNXzp6ksa6aAUEhxH/vJ4yM7vktzt6wvJzkzacSc40x3b7gmVMLyYPAsmsKyVxjzN+0Gmc9sB4gMDwyduHf/tZKVpfL5cge3ZyY68vLDfiID0P9q2mqbwIBnwAfRITgAcFWs3lqeb34h+ZOv/7+f+7t0vROXI/w7VwVVRWYRgO+4DPAB+GbNhFvr9fesLycZOezK/t0IZkPPG+MWeZ+/BMAY8zP2xo/Li7O5OTkeDHhN9LS0hx5KRAn5prw//6K0QPGkN70EGMZyyM8QhNNfBL8Cbl/l2s1m8eWV8tLpnVtcieuR2jOtWjRIrZu3UphYSF72csOdmD45vtkfMh4Tjx9wuu5nLq8nJhLRHqkkDi1jSQbiBKRSBEZADwMbLWcSXVTZNg3u6xKKGEDG3Dh4v7a+zl27JjFZKqzGhsb2bRpE4WFhQydPpQ0v7RvFZFA/0BeWPqCxYTKmxxZSIwxjcCPgY+AQ8CbxpgDdlOp7hoRNIKBfgMZHzIeQQgKCeK2FbcxYtgIXn/9dQoLC21HVB1QWVnJvn37OH78OPfddx9/8+Df8PJ9L19dr+NDxvPyvS+zbuY621GVlzjy8F8AY8x2YLvtHKpn+fn4Xbe7ozamljfeeIN33nmHK1eukJiYqOceONTFixfZuHEj1dXVPPzww0yZ0nwgxLqZ67Rw9GOO3CJR/UvL5VSio6P5+OOP+eijj7Q/Ewc6deoUGzZsoK6ujttuu+1qEVHKsVskqn/x8/PjO9/5DsHBwWRlZVFZWcmqVavw89O3qBMUFxfzl7/8haCgIB599FGKiopsR1IOop9S5RgiwrJlyxgyZAgpKSlUVVXx3e9+l4EDB9qO1q8VFBSwdetWwsPDWbduHcHBdg/VVs6ju7aUo4gIiYmJrF69mq+++opXXnmFiooK27H6JWMMn332Ge+99x6RkZE88cQTWkRUm7SQKEeKiYlh7dq1lJeXs2HDBr2cvJc1NTWxfft2PvnkE2bOnMnatWsJCAiwHUs5lBYS5ViTJk3iiSeeoLGxkQ0bNvDVV1/ZjtQvNDQ08NZbb5GTk8P8+fNZvXq1I8/KVs6hhUQ5WkREBE8++SSBgYG8+uqr7Ny5k4aGBtux+qwvv/ySl156iUOHDnHXXXdx11136aHY6qa0sV05XlhYGD/84Q9JSUkhIyODw4cPX+0XXvWMmpoadu7cSUFBAWFhYTz22GNERkbajqV6CS0kqlcYOHAg9957LzNnzmTbtm3893//N7NmzeLOO+8kMDDQdrxeyxjDwYMH2bFjB9XV1SxYsIDbb79d+xBRnaKFRPUqEyZM4KmnnmL37t2kp6dTXFzM8uXLiY6O1l0wnXT58mW2b9/OF198QUREBI8++igjR460HUv1QlpIVK/j7+/P0qVLiY6OZtu2bWzZsoXCwkLuvvtuQkJCbMdzPGMM2dnZ7Nq1i6amJu68804SEhK0W2PVZVpIVK81cuRInnzySbKyskhNTeV3v/sdS5cuJS4uTr8U23H+/Hm2bdtGSUkJEydO5J577iEsLMx2LNXLaSFRvZqPjw/z58/n1ltv5YMPPmDHjh0UFRVx7733MmLECNvxHKOxsZHPP/+czz77jICAAFatWkVMTIzuDlQ9QguJ6hPCwsJYt24dRUVFfPjhh/zhD39g4cKFLFq0qN9fr6ukpIRt27Zx/vx5Zs6cybJlywgKCrIdS/Uh/fsTpvoUESEmJoZJkybx0UcfsXv3bg4ePMi9997LuHHjbMfzurq6Onbt2kV2djZDhgxh7dq1REVF2Y6l+iArhUREfgncC9QDx4DvG2PKRWQCzR1ZHXGPmmmMecpGRtV7BQUFsWbNGmbOnMkHH3zAK6+8wpw5c5g3b16/2N1VX1/PgQMHSEtLo6Kigrlz57JkyRK9xInyGFtbJCnAT4wxjSLyL8BPgGfczx0zxsyylEv1IVFRUfzoRz/ik08+ITs7m7y8PEaPHs3s2bOJjo7uU1cVNsZQUlJCfn4+Bw4coKGhgfDwcB588EHGjBljO57q46wUEmPMzlYPM4EHbORQfd+AAQNYvnw5ixYtoqioiPz8fN5//30+/PBDpk+fzuzZsxk/frztmF3W0u1tfn4+Fy9eZMCAAcyYMYPZs2czZswYbUxXXuGENpIfAG+0ehwpIvlABfCcMeYzO7FUXxIUFERCQgLz5s3j9OnT5Ofns3//fgoLCwkLCyMkJISKigqGDBliO+pNuVwuiouLyc/Pp7i4GGMM48aNY8GCBURHRzNgwADbEVU/I57q0lREPgbaOk32p8aY99zj/BSIA9YYY4yIBADBxpiLIhILvAtEG2Ou65BCRNYD6wHCw8NjN2/e7JH/42YqKysd2UeDE3P9PKsGl8vFc4nOyOVyubhw4QJnz56lvLwcaD76KyIigmHDhvXIuSiznm7eS1vw64IuTd96PVZVVXH27Fm+/vprGhoaGDBgAOHh4YwcOdLrl4lx4vsLNFdnJScn5xpj4rr7Oh4rJDedscjjwFPAUmNMdTvjpAH/1xiTc6PXiouLMzk5NxzFY9LS0khKSrIy7xtxYq7v/iGD8vJyPnpmhe0o19mxYwcBAQHs27ePiooKBg0aRExMDLNnzyY8PLzrL5zk/pvWtck//vhjhg4dSn5+PqWlpfj4+DBlyhRmz57N5MmTrZ146cT3F2iuzhKRHikkto7aWk5z4/rtrYuIiNwCXDLGuERkIhAFHLeRUfUvgwYNIikpiaSkJI4fP05+fj7Z2dlkZWUxcuRIRo4cSWhoKKGhoYSFhREaGsrgwYNv3AaxcSNkToK6WpjwBLzwAqxb1+aodXV1lJeXU15eTllZ2dW/R48epampieHDh3PnnXcSExPjyF+2qn+z1UbyH0AAkOL+ILYc5rsY+AcRaQRcwFPGmEuWMqp+yMfHh8mTJzN58mSqq6spKiri4MGDHD16lMrKym+N6+vrS0hIyNXC0rrIhO7aReBf/RVS9wEAjadOUf7ss5RXVVE2e/bVotFSMGpqar712v7+/oSGhhIeHs7KlSsZPXq0Npwrx7J11NbkdoZvAbZ4OY5SbQoMDGTevHnMmzcPaL7MyLVbDS2306dPX18Mnn6ax18dRZOPDxv+x3PNA8+cgTNnvlWEIiIiritEgYGBiAhpaWl6+K5yPCcctaVUr+Dn58fw4cMZPnx4m89/a/fUE09QHhpKVdACfF0uklJTCS0rI6y8nNCiopvvFlOqF9FColQPCQgIIDw8vLlx/swZyMwEPgRgUktL3/jx0AsOMVaqM/Ra20p5wgsvwLWH5AYGNg9Xqo/RQqKUJ6xbBy+/3LwFItL89+WX2z1qS6neTHdtKeUp69Zp4VD9gm6RKKWU6hYtJEoppbpFC4lSSqlu0UKilFKqW7SQKKWU6hYtJEoppbpFC4lSSqlu0UKilFKqW6x1bNWTROQ8cNLS7IcDFyzN+0Y0V+dors7RXJ3j1FxTjTGDu/sifeLMdmPMLbbmLSI5PdHDWE/TXJ2juTpHc3WOk3P1xOvori2llFLdooVEKaVUt2gh6b6XbQdoh+bqHM3VOZqrc/p0rj7R2K6UUsoe3SJRSinVLVpIOklEnheRUyJS4L6tbGe85SJyRESOisizXsj1SxE5LCKFIvKOiIS2M94JESlyZ++RIzbamc8N/38RCRCRN9zPZ4nIBE9laTXPsSKSKiKHROSAiPzvNsZJEpHLrdbvzzydyz3fG64XafYb9/IqFJE5Xsg0tdVyKBCRChF5+ppxvLK8RGSDiJwTkf2thg0VkRQRKXb/DWtn2sfd4xSLyONeyGX9s9hOLs99dxlj9NaJG/A88H9vMo4vcAyYCAwA9gHTPZzrLsDPff9fgH9pZ7wTwHAPZ7np/w/8CPi9+/7DwBteWHcRwBz3/cHAF23kSgLet/C+uuF6AVYCOwABEoAsL+fzBc4C420sL2AxMAfY32rYi8Cz7vvPtvWeB4YCx91/w9z3wzycy/pnsZ1cHvvu0i0Sz5gLHDXGHDfG1AObgfs9OUNjzE5jTKP7YSYwxpPzu4mO/P/3A39y338LWCoi4slQxpgzxpg89/0rwCFgtCfn2YPuB14zzTKBUBGJ8OL8lwLHjDFWTvw1xuwGLl0zuPV76E/AqjYmXQakGGMuGWPKgBRguSdzOeGz2M7y6ogufXdpIemaH7s3Wze0szk9Gihp9bgU735h/YDmX69tMcBOEckVkfUemn9H/v+r47g/dJeBYR7Kcx33rrTZQFYbT88XkX0iskNEor0U6WbrxfZ76mFgUzvP2VheAOHGmDPQ/CMBGNHGOLaXm+3P4rU88t3VJ85s72ki8jEwso2nfgq8BPwjzW+CfwT+jeY3y7deoo1pu3143I1yGWPec4/zU6AR2NjOyywwxpwWkRFAiogcdv966Ukd+f89sow6QkSCgS3A08aYimuezqN5902lex/yu0CUF2LdbL3YXF4DgPuAn7TxtK3l1VE2l5sTPouteey7SwtJG4wxd3RkPBH5T+D9Np4qBca2ejwGOO3pXO6GxHuApca9w7ON1zjt/ntORN6heVO2p9+8Hfn/W8YpFRE/IISubYp3ioj401xENhpj3r72+daFxRizXUR+JyLDjTEevU5SB9aLR95THbQCyDPGfH3tE7aWl9vXIhJhjDnj3s13ro1xSmlux2kxBkjzdDAHfRZbz+/q+uvp7y7dtdVJ1+yXXg3sb2O0bCBKRCLdv+YeBrZ6ONdy4BngPmNMdTvjBInI4Jb7NDcKtpW/uzry/28FWo6geQD4pL0PXE9xt8H8EThkjPn3dsYZ2dJWIyJzaf6MXPRwro6sl63AY+6jtxKAyy27dbzgEdrZrWVjebXS+j30OPBeG+N8BNwlImHuXTl3uYd5jMM+i63n6bnvLk8cMdCXb8B/A0VAoXsBR7iHjwK2txpvJc1HBR2jedeTp3MdpXnfZoH79vtrc9F8JMY+9+2AJ3O19f8D/0DzhwtgIPAXd+69wEQvLKOFNG+mF7ZaTiuBp4Cn3OP82L1s9tHcUJrohVxtrpdrcgnwW/fyLALiPJ3LPd9AmgtDSKthXl9eNBeyM0ADzb+an6S5TW0XUOz+O9Q9bhzwX62m/YH7fXYU+L4Xcln/LLaTy2PfXXpmu1JKqW7RXVtKKaW6RQuJUkqpbtFCopRSqlu0kCillOoWLSRKKaW6RQuJUkqpbtFCopRSqlu0kCjlASIS77443kD3WcwHRGSG7VxKeYKekKiUh4jIP9F8Bv8goNQY83PLkZTyCC0kSnmI+1pF2UAtzZcOcVmOpJRH6K4tpTxnKBBMc2+MAy1nUcpjdItEKQ8Rka009zAXSfMF8n5sOZJSHqH9kSjlASLyGNBojHldRHyBdBFZYoz5xHY2pXqabpEopZTqFm0jUUop1S1aSJRSSnWLFhKllFLdooVEKaVUt2ghUUop1S1aSJRSSnWLFhKllFLdooVEKaVUt/z/DiVUEAZITq0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_parabola_from_formula (a, b, c):\n",
    "    plot_parabola(a, b, c)                      # 画曲线\n",
    "\n",
    "    x1 = (-b + (b*b - 4*a*c)**0.5)/(2 * a)\n",
    "    x2 = (-b - (b*b - 4*a*c)**0.5)/(2 * a)\n",
    "\n",
    "    plt.scatter([x1, x2], [0, 0], color=\"green\") # 画解\n",
    "    plt.annotate('x1', (x1, 0))\n",
    "    plt.annotate('x2', (x2, 0))\n",
    "    plt.show()\n",
    "    \n",
    "\n",
    "plot_parabola_from_formula (2, -16, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 函数\n",
    "\n",
    "\\begin{equation}f(x) = x^{2} + 2\\end{equation}\n",
    "\n",
    "\\begin{equation}f(3) = 11\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def f(x):\n",
    "    return x**2 + 2\n",
    "\n",
    "f(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.array(range(-100, 101))\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "plt.grid()\n",
    "\n",
    "plt.plot(x, f(x), color='purple')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## 函数的定义域\n",
    "\n",
    "\\begin{equation}f(x) = x + 1, \\{x \\in \\rm I\\!R\\}\\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}g(x) = (\\frac{12}{2x})^{2}, \\{x \\in \\rm I\\!R\\;\\;|\\;\\; x \\ne 0 \\}\\end{equation}\n",
    "\n",
    "\n",
    "简化形式：\n",
    "\\begin{equation}g(x) = (\\frac{12}{2x})^{2},\\;\\; x \\ne 0\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3600.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def g(x):\n",
    "    if x != 0:\n",
    "        return (12/(2*x))**2\n",
    "\n",
    "x = range(-100, 101)\n",
    "y = [g(a) for a in x]\n",
    "\n",
    "print(g(0.1))\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('g(x)')\n",
    "plt.grid()\n",
    "plt.plot(x, y, color='purple')\n",
    "\n",
    "# 绘制临界点， 如果取接近0的值，临界点附件函数的形状变得不可见\n",
    "plt.plot(0, g(1), color='purple', marker='o', markerfacecolor='w', markersize=8)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "\\begin{equation}h(x) = 2\\sqrt{x}, \\{x \\in \\rm I\\!R\\;\\;|\\;\\; x \\ge 0 \\}\\end{equation}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def h(x):\n",
    "    if x >= 0:\n",
    "        return 2 * np.sqrt(x)\n",
    "\n",
    "x = range(-100, 101)\n",
    "y = [h(a) for a in x]\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('h(x)')\n",
    "plt.grid()\n",
    "\n",
    "plt.plot(x, y, color='purple')\n",
    "# 画出边界\n",
    "plt.plot(0, h(0), color='purple', marker='o', markerfacecolor='purple', markersize=8)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "\n",
    "\\begin{equation}j(x) = x + 2,\\;\\; x \\ge 0 \\text{ and } x \\le 5\\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}\\{x \\in \\rm I\\!R\\;\\;|\\;\\; 0 \\le x \\le 5 \\}\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def j(x):\n",
    "    if x >= 0 and x <= 5:\n",
    "        return x + 2\n",
    "\n",
    "x = range(-100, 101)\n",
    "y = [j(a) for a in x]\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('j(x)')\n",
    "plt.grid()\n",
    "\n",
    "plt.plot(x, y, color='purple')\n",
    "\n",
    "# 两个边界点\n",
    "plt.plot(0, j(0), color='purple', marker='o', markerfacecolor='purple', markersize=8)\n",
    "plt.plot(5, j(5), color='purple', marker='o', markerfacecolor='purple', markersize=8)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 阶梯函数\n",
    "\n",
    "\\begin{equation}\n",
    "k(x) = \\begin{cases}\n",
    "  0, & \\text{if } x = 0, \\\\\n",
    "  1, & \\text{if } x = 100\n",
    "\\end{cases}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def k(x):\n",
    "    if x == 0:\n",
    "        return 0\n",
    "    elif x == 100:\n",
    "        return 1\n",
    "\n",
    "x = range(-100, 101)\n",
    "y = [k(a) for a in x]\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('k(x)')\n",
    "plt.grid()\n",
    "\n",
    "\n",
    "plt.scatter(x, y, color='purple')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 函数的值域\n",
    "\\begin{equation}p(x) = x^{2} + 1\\end{equation}\n",
    "\n",
    "\\begin{equation}\\{p(x) \\in \\rm I\\!R\\;\\;|\\;\\; p(x) \\ge 1 \\}\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def p(x):\n",
    "    return x**2 + 1\n",
    "\n",
    "x = np.array(range(-100, 101))\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('p(x)')\n",
    "plt.grid()\n",
    "\n",
    "plt.plot(x, p(x), color='purple')\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  },
  "livereveal": {
   "scroll": true
  },
  "rise": {
   "enable_chalkboard": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
